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Sufficient Conditions for the Existence and Uniqueness of Minimizers for Variational Problems under Uncertainty

Author

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  • Mansi Verma

    (Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, Malaysia
    These authors contributed equally to this work.)

  • Chuei Yee Chen

    (Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, Malaysia
    These authors contributed equally to this work.)

  • Adem Kılıçman

    (Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, Malaysia)

  • Gafurjan Ibragimov

    (Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, Malaysia)

  • Fong Peng Lim

    (Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, Malaysia)

Abstract

Fuzzy variational problems have received significant attention over the past decade due to a number of successful applications in fields such as optimal control theory and image segmentation. Current literature on fuzzy variational problems focuses on the necessary optimality conditions for finding the extrema, which have been studied under several differentiability conditions. In this study, we establish the sufficient conditions for the existence of minimizers for fuzzy variational problems under a weaker notion of convexity, namely preinvexity and Buckley–Feuring differentiability. We further discuss their application in a cost minimization problem.

Suggested Citation

  • Mansi Verma & Chuei Yee Chen & Adem Kılıçman & Gafurjan Ibragimov & Fong Peng Lim, 2022. "Sufficient Conditions for the Existence and Uniqueness of Minimizers for Variational Problems under Uncertainty," Mathematics, MDPI, vol. 10(19), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3638-:d:933829
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    References listed on IDEAS

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    1. Panigrahi, Motilal & Panda, Geetanjali & Nanda, Sudarsan, 2008. "Convex fuzzy mapping with differentiability and its application in fuzzy optimization," European Journal of Operational Research, Elsevier, vol. 185(1), pages 47-62, February.
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